You can't really use a lookup to "set" the value of a dropdown like you do with other field types, that will only set the "list" of values.

When there is only one result value, it is essentially the same since it auto-selects the only value available, but what it is really doing is populating the list of options not setting a specific value.

I imagine the reason it doesn't look like your Append selection is doing anything is because I believe there is some built in functionality to prevent duplicate options.

If you want to preserve the list and auto-select a value in a dropdown using the results of a lookup, then you'll need to utilize a separate hidden field.

Basically, create a hidden single line field that receives the lookup result value, then add JavaScript that will "transfer" that value to your dropdown whenever it changes.

for example,

$(document).ready(function(){
   $('.myLookup input').on('change', function(){
       $('.myDropdown select').val($(this).val()).change();
   });
});